基于Eigen Decomposition FrFT双绞线检测系统设计

Design of a Twisted Pair Detection System Based on Eigen Decomposition FrFT

摘要: 在远距离双绞线电缆故障诊断的过程中，故障诊断的准确性容易受到实际环境中的多种因素影响，在采集反射信号时，会受到噪音等因素的影响，造成采集频率不准确、搜索误差较大等影响，最终影响了电缆诊断系统的准确性。分数阶傅里叶变换(Fractional Fourier Transform, FRFT)是一种新型电缆故障检测方法，利用线性调频信号(LFM signal)作为入射信号，由于FrFT对LFM信号在特殊阶数下产生能量聚集性的特点，在分数域中可以检测到故障位置的冲激函数，因此可以得到故障位置。近年来，离散分数阶傅里叶变换的发展，衍生出了最接近连续分数阶傅里叶性质的特征分解型傅里叶变换。经实验验证，在最佳Hermite-Gaussian函数近似值下能够得到比采样型FrFT的更好的检测效果。

Abstract: In the process of long-distance twisted pair cable fault diagnosis, the accuracy of fault diagnosis is easily affected by various factors in the actual environment. When collecting reflected signals, it is affected by factors such as noise, resulting in inaccurate collection frequency and large search er-rors, ultimately affecting the accuracy of the cable diagnosis system. Fractional Fourier Transform (FRFT) is a novel cable fault detection method that utilizes linear frequency modulation (LFM signal) as the incident signal. Due to the energy aggregation of the LFM signal under special orders, FRFT can detect the impulse function of the fault location in the fractional domain, thus obtaining the fault location. In recent years, with the development of discrete fractional Fourier transform, the Eigende composition of a matrix Fourier transform, which is closest to the continuous fractional Fourier transform, has been derived. Through experimental verification, better detection performance can be achieved than the sampled FrFT under the optimal Hermite Gaussian function approximation.